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Big Ideas Math: Modeling Real Life, Grade 6

BI

Big Ideas Math: Modeling Real Life, Grade 6 View details

3. Solving Equations Using Multiplication or Division

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Exercise 3 Page 263

Use the Subtraction Property of Equality to eliminate the addition.

p=5/8

Practice makes perfect

To solve the equation, we have to isolate p on one side. Using the Subtraction Property of Equality we will subtract 14 from both sides of the equation. This will eliminate addition and isolate p.

7/8=1/4+p

LHS-1/4=RHS-1/4

7/8-1/4=1/4-1/4+p

1/4-1/4=0

7/8-1/4=p

a/b=a * 2/b * 2

7/8-1* 2/4* 2=p

Multiply

7/8-2/8=p

Subtract fractions

7-2/8=p

Subtract term

5/8=p

Rearrange equation

p=5/8

To check that this solution is correct, let's substitute p= 58 into the original equation and simplify.

7/8=1/4+p

p= 5/8

7/8? =1/4+ 5/8

a/b=a * 2/b * 2

7/8? =1* 2/4* 2+5/8

Multiply

7/8? =2/8+5/8

Add fractions

7/8? =2+5/8

Add terms

7/8=7/8 ✓

Since the left-hand side and right-hand side are equal, p= 58 is the correct solution.

Extra

Properties of Equality

There are four main Properties of Equality that we use when solving linear equations.

Properties of Equality
Addition Property of Equality	If a=b, then a+c=b+c.
Subtraction Property of Equality	If a=b, then a-c=b-c.
Multiplication Property of Equality	If a=b, then ac=bc.
Division Property of Equality	If a=b and c is not 0, then a/c=b/c.

In later chapters, you will learn about some more advanced Properties of Equality. As an example, there is a property for when we need to eliminate a radical or an exponent.

Power Property of Equality
If a=b, then a^m=b^m.

Subchapter links

Try It p.260-261

Self-Assessment for Concepts & Skills p.261

Self-Assessment for Problem Solving p.262

Review & Refresh p.263

Concepts, Skills, & Problem Solving p.263-264